What determines which stage occurs after a supernova?

A supernova is the brilliant explosion of a star that has reached the end of its life. Both the lifespan of a star and its final state are determined by the mass of the star. For a low mass star, gravity is not strong enough to start fusion again and the burnt out star becomes a brown dwarf and eventually a cold dead body in space. If the mass of the star is great, near the mass of the sun, gravitational force is great enough to squeeze the center and make it hot enough for the star to start fusing helium into other light elements. This renewed energy causes the star to swell into a red giant, appearing as a planetary nebula.